Numerical simulation of a tropical Storm boundary layer

A model has been designed to study the surface boundary layer of a tropical storm. The numerical method consists of solving a two point boundary value problem for two systems of simultaneous non-linear differential equations by finite differences. A Stoke's stream function suitable to represent the flow both in interior and exterior regions of a tropical storm boundary layer has been developed. The advantage of the method is that the, boundary layer of the tropical storm can be studied starting from the outer region to the centre of the storm without neglecting non-linear terms. In addition, there IS no need for assumptions on the vertical profiles for tangential and radial velocities. The method is stable and converges within a few iterations. The flow above the friction layer is represented by a steady axisymmetric vortex in gradient balance. To investigate the effect of turbulence- on boundary layer characteristics, turbulence has been represented by four different variations of the eddy coefficient of viscosity with no slip boundary conditions. Computations have been performed 1aking 40-grid points in the vertical direction. It is observed that, if the eddy coefficient of viscosity is assumed to vary with the superimposed flow above the boundary layer, the solutions compare favourably well with observations. The solution also shows an outflow from the Inner core of the boundary layer which is necessary for creation of an eye of the storm.

Radial and vertical velocity field in a steady state symmetric tropical storm

ABSTRACT. A method to construct a consistent structure of steady state symmetric tropical storms from a few known values of temperature anomaly in the centre and around it has been developed. The role of kinematic eddy coefficient of viscosity in producing the transverse circulation in a tropical storm has been tested and discussed. The well known features and characteristics of a tropical storm, such as, eyewall, sinking motion, inside the eyewall, low-level radial inflow and high level outflow are well produced in the model. The computation shows that there is an increase of transverse circulation with increase of the magnitude of eddy coefficient. In the boundary layer, the vertical eddy coefficient plays more important role than the radial eddy coefficient; while in the upper layer the latter is much more important than the former. It has also been found that in absence of radial exchange coefficient, there can be no sinking motion in the central region of the storm. The magnitude of radial and vertical wind in the eye region is more sensitive to the variation of radial eddy coefficient. In addition to the eddy coefficients, transverse circulations also depend upon the tangential wind distribution above the boundary layer.

Duncan Dowson’s impact on industrial tribology

Professor Duncan Dowson had close connections with industry throughout his academic career, and viewed industrial tribological challenges as problems to be solved and as a source of new ideas. Professor Dowson’s famous work on a numerical solution for the lubrication of an elastohydrodynamic line contact, with professor Higginson, was motivated by the need to better understand gear lubrication. These first calculations took 18 months to complete(!), and simpler correlation functions fitted to numerical simulations were developed to enable tribologists in academia and industry to apply elastohydrodynamic lubrication theory without the need for full scale models. Industrial partners such as Shell supplied high-pressure fluid properties required for the elastohydrodynamic calculations (such as the pressure coefficient of viscosity and the way in which lubricant density varies with pressure). Professor Dowson also famously served on the Jost Committee, which quantified, for the first time, the financial impact of tribology, and highlighted that investments in good tribological practices would pay for themselves many times over. It should be remembered that in setting up the Jost Committee, the UK Government specifically asked the committee ‘ to investigate the state of lubrication education and research and to establish the requirements of industry in this regard’. Personal memories of the significant collaborations that I was involved with, as an industrial research scientist, with Leeds University from the mid-1990s to around 2013, which predominantly focused on piston ring tribology are also included as is a brief discussion of the Leeds-Lyon Symposia on Tribology.

Laboratory Investigations of the Bending Rheology of Floating Saline Ice and Physical Mechanisms of Wave Damping in the HSVA Hamburg Ship Model Basin Ice Tank

An experimental investigation of flexural-gravity waves was performed in the Hamburg Ship Model Basin HSVA ice tank. Physical characteristics of the water-ice system were measured in several locations of the tank with a few sensors deployed in the water and on the ice during the tests. The three-dimensional motion of ice was measured with the optical system Qualisys; water pressure was measured by several pressure sensors mounted on the tank wall, in-plane deformations of the ice and the temperatures of the ice and water were measured by fiber optic sensors; and acoustic emissions were recorded with compressional crystal sensors. The experimental setup and selected results of the tests are discussed in this paper. Viscous-elastic model (Burgers material) is adopted to describe the dispersion and attenuation of waves propagating below the ice. The elastic modulus and the coefficient of viscosity are calculated using the experimental data. The results of the measurements demonstrated the dependence of wave characteristics from the variability of ice properties during the experiment caused by the brine drainage. We showed that the cyclic motion of the ice along the tank, imitating ice drift, and the generation of under ice turbulence cause an increase of wave damping. Recorded acoustic emissions demonstrated cyclic microcracking occurring with wave frequencies and accompanying bending deformations of the ice. This explains the viscous and anelastic rheology of the model ice.

RHEOLOGICAL MODELING OF THE STRESS-STRAIN STATE IN FLAT COMPACTION OF COMPOSITE MATERIALS

Statement of the problem. The article investigates the deformation behavior of a composite material in the process of its flat pressing. To solve this problem, a rheological model is proposed, which is based on the phenomena occurring in a viscous (Newtonian) incompressible fluid, which occupies the volume between two absolutely rigid parallel planes of finite dimensions of rectangular shape approaching at a low speed. Within the framework of mechanics of a continuous medium under conditions of a plane deformed state, the problem is solved in two dimensions about a slow flow in the absence of volume forces and inertial effects. In this case, the solution of the equation of motion with continuity conditions is reduced to the well-known Laplace equation. In addition, on the basis of the model of linear viscoelasticity and uniaxial stress state, an attempt has been made to describe the relaxation phenomena occurring in the solidifying composite at the end of the active pressing process. Results and Conclusions. Analytical dependences of the power parameters of the stress-strain state of the compressed composite are obtained; relations for the kinematic characteristics of the pressing process are obtained; an expression is obtained for the relaxation of stresses during the technological holding of the material under pressure after the end of active pressing. The results of the study make it possible to experimentally determine the numerical values of the dynamic coefficient of viscosity and stress relaxation time, which are important characteristics in controlling the pressing processes.

RHEOLOGICAL MODELING OF THE STRESS-STRAIN IN FLAT COMPACTION OF COMPOSITE MATERIALS

Постановка задачи. В статье исследуется деформационное поведение композиционного материала в процессе его плоского прессования. Для решения этой проблемы предложена реологическая модель, в основе которой лежат явления, протекающие в вязкой (ньютоновской) несжимаемой жидкости, занимающей объем между двумя сближающимися с малой скоростью абсолютно жесткими параллельными плоскостями конечных размеров прямоугольной формы. В рамках механики сплошной среды в условиях плоского деформированного состояния решается задача в двух измерениях о медленном течении в отсутствии объемных сил и инерционных эффектов. При этом решение уравнения движения с условиями неразрывности сводится к известному уравнению Лапласа. Кроме того, на основе модели линейной вязкоупругости и одноосного напряженного состояния предпринята попытка описания релаксационных явлений, протекающих в затвердевающем композите по окончании процесса активного прессования. Результаты и выводы. Получены аналитические зависимости силовых параметров напряженно-деформированного состояния прессуемого композита; получены соотношения для кинематических характеристик процесса прессования; получено выражение для релаксации напряжений в процессе технологической выдержки материала под давлением после окончания активного прессования. Результаты исследования позволяют экспериментально определять численные значения динамического коэффициента вязкости и времени релаксации напряжения, которые являются важными характеристиками при управлении процессами прессования. Statement of the problem. The article investigates the deformation behavior of a composite material in the process of its flat pressing. To solve this problem, a rheological model is proposed which is based on the phenomena occurring in a viscous (Newtonian) incompressible fluid that occupies the volume between two absolutely rigid parallel planes of finite dimensions of rectangular shape approaching at a low speed. Within the framework of mechanics of a continuous medium under conditions of a plane deformed state, the problem is addressed in two dimensions about a slow flow in the absence of volume forces and inertial effects. In this case, the solution of the equation of motion with continuity conditions is reduced to the well-known Laplace equation. In addition, based on the model of linear viscoelasticity and uniaxial stress, an attempt has been made to describe the relaxation phenomena occurring in the solidifying composite at the end of the active pressing process. Results and conclusions. Analytical dependences of the power parameters of the stress-strain of the compressed composite are obtained; relations for the kinematic characteristics of the pressing process are identified; an expression is designed for the relaxation of stresses during the technological holding of the material under pressure following the end of active pressing. The results of the study make it possible to experimentally determine the numerical values of the dynamic coefficient of viscosity and stress relaxation time which are important characteristics in controlling the pressing processes.

Passing Lecture On The Topic" Fluid Flow And Biophysical Properties " In The Online System

This article is devoted to the transition of"fluid flow and biophysical properties" in the module system. It is stated that it is possible to find the coefficient of viscosity in the Stox method, the coefficient of viscometric methods, to find the coefficient of viscosity in the axiom of Medicine, in diagnosis and in medical and forensic expertise. It is also described to find the coefficient of processes and surface tension on the surface of liquids by drip method.

Time dependence of advection-dominated accretion flow around a rotating compact object

ABSTRACT Time evolution of advection-dominated accretion flow (ADAF) around a rotating compact object is presented. The time-dependent equations of fluid including the Coriolis force along with the centrifugal and pressure gradient forces are derived. In this research, it is assumed that angular momentum transport is due to viscous turbulence and the α-prescription is used for the kinematic coefficient of viscosity. Moreover, the general relativistic effects are neglected. In order to solve the equations, we have used a self-similar solution. The solutions show that the behaviour of the physical quantities in a dynamical ADAF is different from that for a steady accretion flow. Our results indicate that the physical quantities are dependent of rotation parameter which is defined as the ratio of the intrinsic angular velocity of the central body to the angular velocity of disc. Also, the effect of rotation parameter on these quantities is different for co and counter-rotating flows. The solution shows that by increasing the rotation parameter a, inflow–outflow region approaches the central object for co-rotating flow and moves outwards for counter-rotating flow. We find that when flow is fully advection dominated (f → 1), the entire gas has positive Bernoulli function. Also, we suggest that the Bernoulli function becomes more positive when the effect of rotation on the structure of disc decreases.

DETERMINATION OF VISCOSITY OF WILD MANGO (Irvingia gobonensis), HIBISCUS (Rosa sinensis) AND OKRO (Abelmoschus esculentus) AT DIFFERENT TEMPERATURES

Viscosity is an important factor in fluid transport. It is a quantity that influences flow properties of fluid and quite useful food product designs. This study is aim at determining the viscosity of selected plant based materials, Wild mango, Hibiscus and Okro and to obtain a viscosity temperature model necessary to predict viscosity of these materials at various temperature values. The viscosity of these materials were determined using the volume flow rate method at a temperature range between 299k to 383k and the viscosity temperature model obtained from an empirical relationship. Wild mango exhibited the highest value of coefficient of viscosity at all temperature range with values between 18.3 x 10-3NSm-2 to 5.45 x 10-3 NSm-2 while Hibiscus and Okro have values of coefficient of viscosity ranging between 6.69 x 10-3NSm-2 to 1.82 x 10-3 NSm-2 and 8.05 x 10-3NSm-2 to 2.10 x 10-3 NSm-2 respectively. The coefficients of viscosity of these materials were found to decrease with increase in temperature. The viscosity temperature model obtained for wild mango, Hibiscus and Okro are , and respectively KEY WORDS: Viscosity, temperature, Wild mango, Hibiscus, Okro